Constrainedand

Constrainedand is a term used in constraint programming and constrained logic to denote a conjunction of two predicates or conditions that must hold under a shared set of variable constraints. It is not a standardized operator in mainstream logic; rather, it appears in some domain-specific languages and research discussions as a convenient way to express that two conditions hold simultaneously while the variables involved are subject to additional restrictions.

Formal characterization of constrainedand treats the operation as the combination of two predicates A and B with an accompanying constraint set C on the involved variables. In practice, constrainedand(A, B; C) is interpreted as solving A and B under the constraint store that includes C. If a solver finds an assignment to the variables that satisfies A, B, and all constraints in C, the instance is satisfiable; otherwise it is unsatisfiable. When C is empty, constrainedand reduces to the ordinary logical conjunction A ∧ B.

Implementation-wise, constrainedand is typically realized by augmenting the constraint-solving process with the additional constraints C and requiring both sub-predicates A and B to be satisfied within that augmented system. This mirrors how constraint solvers handle conjunctions: they propagate and prune domains while maintaining a consistent set of constraints across all involved variables.

Example: let A be x > 0, B be y = 2x, and C be x + y = 7. Constrainedand(A, B; C) seeks real values x and y satisfying all three, yielding x = 7/3 and y = 14/3 as a solution.

Constrainedand is useful for modeling problems where multiple conditions must be true in the presence of shared variable constraints, such as optimization, scheduling, and formal verification. It remains a descriptive concept rather than a universal operator, with implementation details varying by language or solver. See also conjunction, constraint programming, and constraint satisfaction problems.